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The present invention relates to synchronous frame current regulators and more specifically to an adaptive predictive current regulator that increases system bandwith while maintaining current overshoot within an acceptable range.
In virtually any control environment the goal is to cause a specific result instantaneously when a specific command signal is provided. While the stated goal is simple, the solution for achieving the stated goal often is much more complex as hardware required to facilitate instantaneous results often have unknown or variable characteristics and hardware controlling systems often cause processing delays that are difficult to eliminate.
One area of the controls industry in which precise control is particularly important is in motor control or control of other inductive type machines. In these cases often even a slight delay in system control can result in loss of motor control, motor and control system damage or expedited degradation. For this reason many motor control systems include several different control or feedback loops that compare command signals to resulting signals to generate error signals and then adjust the command signals as a function of the error signals in an effort to eliminate the control error.
To this end vector motor drives include a current regulator as an innermost control loop with other control loops nested around the current regulator. Because other loops are nested around the current regulator any error generated by the current regulator can be exacerbated by the other loops. For this reason the current regulator typically needs to be extremely accurate and highly responsive.
As well known in the controls industry, most vector drives perform current regulation on electrical reference frame variables to ensure zero steady state error. Electrical reference frame variable regulators are commonly referred to in the motor control industry as synchronous frame current regulators (SFCRs).
Referring to FIG. 1, a typical SFCR in the sampled data and continuous domain system 10 is illustrated that includes a plurality of blocks that together model an inductive load and associated control system. All of the events and calculations in FIG. 1 occur inside a microprocessor or within other motor drive or motor hardware controlled by the processor. Nevertheless, system 10 is represented as discrete events and calculations in order to generate transfer functions and current predicting equations that must be understood for a thorough understanding of the present invention.
System 10 includes first and second summers 12, 14, respectively, a proportional-integral (PI) compensator 16, a unit sample delay 18, a zero order hold (ZOH) 20, a pulse width modulator (PWM) gain block 22, a plant xe2x80x9ceffectxe2x80x9d model or block 24 and a sampler 26.
First summer 12 receives each of a current command signal i*(z) and a sampled current signal i(z) and subtracts the sampled signal from the command signal to generate a current error signal Er. Pi compensator 16 receives error signal Er and steps that signal up as a function of a PI gain factor Kpi thereby generating a voltage adjustment signal V(z). The PI compensator 16 function can be expressed as:                                           k            pi                    ⁡                      (                          z              -                              δ                c                                      )                                    z          -          1                                    Eq. 1            
Second summer 14 receives the voltage adjustment signal V(z) and a voltage feedforward signal Vff(z) from another control loop sampler (not illustrated) and adds the received signals to generate an adjusted voltage signal V(z)xe2x80x2.
The unit sample delay 18 and the ZOH 20 are provided in system 10 to represent the finite update rate of practical conventional control loop configurations.
Voltages having specific amplitudes and frequencies are generated using PWM inverters. As well known in the motor controls industry a PWM inverter typically includes a plurality of switching devices that alternately link positive and negative DC buses to output lines thereby causing a series of positive and negative voltage pulses on the output lines. The average of the voltage pulses over a PWM cycle causes an alternating voltage at the output. Where a load is linked to the output the alternating voltage causes an alternating current across the load. PWM block 22 represents the gain effects of a conventional PWM inverter as represented by a gain factor Kpwm. The effect of block 22 is to modify the received signal by factor Kpwm. The output of block 22 is provided to plant block 24.
Every plant or load linked to PWM inverter outputs has some effect on the current provided to the plant. For example, where the plant is inductive (e.g., in the case of an induction motor), current provided to the plant cannot change immediately and therefore, even where an inverter is controlled to cutoff voltage to the plant, the inductive plant will still draw some current from the inverter. In general, the effect of a plant on received current is a function of both load resistance rs and load inductance L and can be expressed in the continuous domain by the equation:                               1                      r            s                                    1          +                      s            ⁢                          xe2x80x83                        ⁢            τ                                              Eq. 2            
where xcfx84 equals a load time constant L/rs. Thus, xe2x80x9cplant effectxe2x80x9d is modeled as illustrated in block 24 and current i(t) represents the current provided to the plant via a PWM inverter.
Referring to FIGS. 1 and 1a, system 10 can be represented in the z-domain as two gain blocks Gcomp(z) and Gplant(z). In FIGS. 1a and 1 similarly numbered components are identical.
Sampler 26 links the plant current i(z) to first summer 12 and samples the plant current i(z) at intervals T, providing a new sampled current i(t) every T interval.
Referring still to FIG. 1, the positions of the feedforward sampler (i.e., providing Vff(z)) and feedback sampler 26 result in an explicit transfer function between the current command i*(z) and current feedback i(z) such that the overall system gain G(s) can be expressed as: G(s)=Gcomp(z)*Gplant(z). It is customary to set the proportional and integral gains of the PI compensator so as to cancel the dominant dynamics (i.e., the pole) of the plant, which are typically the slowest dynamic in a practical control system. If such a pole-zero cancellation is assumed, the current regulator/R-L load reduces to a second order system with an open loop transfer function G(z) expressed as:                               G          ⁡                      (            z            )                          =                                                            K                pi                            ⁢                                                                    K                    PWM                                    ⁡                                      (                                          1                      -                                              ⅇ                                                                              -                            T                                                    /                          τ                                                                                      )                                                  /                                  r                  s                                                                    z              ⁡                              (                                  z                  -                  1                                )                                              =                                    i              ⁡                              (                z                )                                                                    i                *                            ⁡                              (                z                )                                                                        Eq. 3            
Thus, the closed loop transfer function of system 10 in FIG. 1 has two poles at locations governed by the PI compensator gain Kpi. As compensator gain Kpi is increased the poles in Equation 3 depart from the real axis, an occurrence that indicates an undesirable oscillatory characteristic.
As well known in the motor controls industry oscillation problems are exacerbated as the system operating bandwidth is increased. When the operating bandwidth includes relatively high frequencies overshoot is increased. Thus, one solution for dealing with second order system overshoot and resulting oscillations is to reduce the system operating bandwidth. Unfortunately, when bandwidth is reduced response time is increased (i.e., settling time is increased).
Another solution for dealing with oscillations in a second order system is to provide a predictor that acts as a unit sample advance in the current feedback loop. A unit sample advance 28 in the feedback loop is illustrated in FIG. 2 where block 30 represents blocks 16, 18, 20, 22 and 24 and summer 14 from FIG. 1. The open loop gain Gp(z) of the current regulator in FIG. 2 can be expressed as:                                           G            p                    ⁡                      (            z            )                          =                                            K              pi                        ⁢                                                            K                  PWM                                ⁡                                  (                                      1                    -                                          ⅇ                                                                        -                          T                                                /                        τ                                                                              )                                            /                              r                s                                                          (                          z              -              1                        )                                              Eq. 4            
Thus, the current regulator 10xe2x80x2 of FIG. 2 operates as a first order system cascaded with a unit sample delay, thereby decoupling the dynamics of the computation delay from those of PI compensator 16 (see FIG. 1). System 10xe2x80x2 closed loop poles do not depart from the real axis, a characteristic that indicates an essentially first order response. In fact, the gain of the PI compensator can now be increased to a high enough value to achieve a dead beat response, a threefold improvement in the responsiveness of the current loop.
Referring again to FIG. 1, an R-L load corresponding to plant model 24 forms a first order system and as such its behavior can be predicted from a knowledge of its initial condition (i.e., initial current i(z)) and a forcing function (i.e., the applied voltage). In FIG. 1, using the notation employed above in Equations 3 and 4, the current at sampling instant k+1 can be expressed as:                               i          ⁡                      (                          k              +              1                        )                          =                                            i              ⁡                              (                k                )                                      ⁢                          ⅇ                                                -                  T                                /                τ                                              +                                    V              ⁡                              (                                  k                  -                  1                                )                                      xc3x97                                          (                                  1                  -                                      ⅇ                                                                  -                        T                                            /                      τ                                                                      )                                            r                s                                      xc3x97                          K              PWM                                                          Eq. 5            
For typical control system implementations load time constant xcfx84 is far larger than the sampling interval T. For this reason Equation 5 can be further simplified as:
i(k+1)=i(k)xc3x97(1xe2x88x92rsT/L)+V(kxe2x88x921)xc3x97KPWMT/Lxe2x80x83xe2x80x83Eq. 6
where L=load inductance.
Equation 6 constitutes the predictor equation used to introduce the unit sample advance in the feedback path as shown in FIG. 2. The use of such a predictor equation, however, necessitates an accurate estimate of load time constant xcfx84(i.e., xcfx84=L/rs) and resistance rs. Inaccuracies in these estimates can lead to steady state errors, and, in extreme cases can cause oscillatory behavior.
Estimating the time constant xcfx84 and resistance rs is not an easy task and often requires highly skilled engineers to render acceptable estimated values. For this reason commissioning of regulators that require accurate time constant xcfx84 and resistance rs estimates is relatively expensive.
Thus, there is a need for a system that eliminates the need for accurate time constant xcfx84 and resistance rs estimates that is inexpensive and computationally simple to implement.
The present inventors have recognized that, in addition to providing a predictor in a feedback loop, an adjuster can also be provided that, based on a comparison of an actual current and the predicted current, can modify the forcing function to expedite regulator response time without requiring accurate time constant xcfx84 and resistance rs estimates.
To this end, an exemplary embodiment of the invention is used with a current regulator and an inverter to provide current to an induction machine. The regulator includes a summer and a PI compensator. The summer subtracts a predicted current signal from a current command signal to generate an error signal. The compensator receives and modifies the error signal to generate a forcing signal used to control the inverter. The inventive apparatus includes a sampler linked to motor supply lines for sampling the actual current and providing a sampled current signal, a predictor that receives the sampled signal and the forcing signal and mathematically combines the sampled and forcing signals to generate a predicted current signal. An adapter receives the predicted current signal and the sampled signal and when the predicted signal is greater than the sampled signal, causes the predictor to reduce the predicted signal and, when the predicted signal is less than the sampled signal, causes the predictor to increase the predicted signal.
When the predicted signal is not equal to the actual sampled current signal clearly assumptions manifest in the computations that implement the predictor are inaccurate and the predicted current signal should be modified. More specifically, the predicted signal should be altered so that the predicted signal more closely resembles the actual sampled signal as required by the present invention.
Thus, one object of the invention is to provide a predictive current regulator that automatically identifies when a predicted current calculating algorithm is inaccurate and adjusts the predicted current signal appropriately.
A related object of the invention is to eliminate the need for a highly skilled engineer to program a current regulator with resistance rs and time constant xcfx84 value estimates. Because the inventive system modifies the predictor calculation based on perceived inaccuracies in the calculation, even where relatively inaccurate system value estimates are provided to the regulator, the regulator will compensate appropriately.
One other related object is to reduce current overshoot and setting time. To this end, the predicted signal adjustments cause the PI compensator to generate a forcing function that drives the plant current to the commanded value much more quickly than in systems that do not employ such control tactics.
By adjusting the predicted signal value to be more like the sampled current value, regulator operation is affected in two related ways that tend to reduce overshoot and settling time. First, the summer and PI compensator generate a modified gain that adjusts the forcing function to ensure zero steady-state error between the predicted and sampled current. For example, where the predicted current is greater than the sampled current the forcing function is decreased to ensure the predicted current equals the sampled current in steady-state. Second, because the gain now more closely reflects the actual system gain the predicted current will more closely represent the future system current in the next cycle and will reduce potential current overshoot.
These and other objects, advantages and aspects of the invention will become apparent from the following description. In the description, reference there is shown a preferred embodiment of the invention. Such embodiment does not necessarily represent the full scope of the invention and reference is made therefor, to the claims herein for interpreting the scope of the invention.